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I enjoy basketball. It’s a fast-paced competitive game and I’ve enjoyed both playing and watching it for a long time. The NBA is famous for generating very clean data, which has long been used by enthusiasts (like myself) for data visualizations, modeling and game predictions.

我喜欢篮球。 这是一款快节奏的竞技游戏，很长时间以来我都喜欢玩和观看它。 NBA以生成非常干净的数据而闻名，长期以来，发烧友(如我自己)一直将其用于数据可视化 ， 建模和游戏预测 。

Recently, I was contacted by DraftKings regarding an interview for a potential job. As part of my preparations for the same, I started using their platform and competing in mock competitions to get acquainted with the DraftKings (DK) contest process. It was during this time period that I really started getting into the idea of using data to model and predict a winning roster.

最近， DraftKings就某项潜在工作的面试与我联系。 作为准备工作的一部分，我开始使用他们的平台并参加模拟竞赛，以了解DraftKings(DK)竞赛过程。 正是在这段时间里，我才真正开始使用数据建模和预测获胜者名单的想法。

I built the algorithm iteratively, and from scratch- starting with a naive version 1, a more robust version 2 and currently I’m working on a winning version 3.

我迭代地构建了算法，从零开始，从朴素的版本1开始，是功能更强大的版本2，目前我正在开发获奖的版本3。

I built the algorithm iteratively, and from scratch

我从头开始迭代构建算法

You can follow along my algorithm design journey in the rest of the article.

您可以在本文的其余部分中继续我的算法设计过程。

快速级别设置：评分和规则 (Quick Level Set: Scoring and Rules)

DK’s rules and scoring for their NBA classic fantasy contests are fairly intuitive, even if you have no prior basketball knowledge. In a nutshell, the objective is to:

即使您没有篮球知识，DK的NBA经典幻想比赛规则和得分也非常直观。 简而言之，目标是：

Create an 8-player lineup while staying under the $50,000 salary cap.

创建一个8人游戏阵容，同时将工资保持在50,000美元以下。

Players get different points for different actions (more details below) and the draft with the most number of points, at the end of all games in a night, wins. Sounds simple enough :)

玩家在不同的操作中获得不同的分数(更多详细信息，请参见下文)，并且在一夜内所有游戏结束时，得分最高的选秀会获胜。 听起来很简单:)

The breakdown for different actions that result in positive (or negative) points can be seen below.

导致正(或负)分的不同动作的细分如下所示。

One last constraint which makes drafting slightly more complicated is player positions. According to DK: Lineups will consist of 8 players and must include players from at least 2 different NBA games.

最后一个使选秀稍微复杂一些的约束是球员位置。 根据DK： 阵容将由8名球员组成，并且必须包括至少2场不同NBA游戏中的球员。

Further, the 8 players are broken down by positions, which can be seen below.

此外，这8个玩家按位置细分，如下所示。

There you have it! A simple optimization problem with a set of constraints. Sounds like something an algorithms would excel at. Or would it?

你有它！ 具有一组约束的简单优化问题。 听起来像算法会擅长的事情。 还是会？

算法版本1-天真 (Algorithm Version 1- Naive)

My goal with this algorithm was to build it as fast as possible, with little to no hopes of winning. Mainly because I was interested in setting up a strong foundation, without worrying about building complex logic early in the process. To do this, I downloaded a player dataset from DK and started a Jupyter notebook. If you’re interested, you can find the full raw data here and my notebook here.

我使用此算法的目标是尽可能快地构建它，几乎没有希望获胜。 主要是因为我有兴趣建立一个强大的基础，而不必担心在此过程的早期就构建复杂的逻辑。 为此，我从DK下载了播放器数据集并启动了Jupyter笔记本。 如果你有兴趣，你可以找到完整的原始数据， 在这里 ，我的笔记本电脑在这里 。

Let’s see what our data looks like.

让我们看看我们的数据是什么样的。

Right off the bat, we can tell that for a simple algorithm, given our requirements and constraints, we’ll find the following columns useful: ID, Salary and AvgPointsPerGame (fantasy points). This would allow us to pick the “best” players while staying under the $50,000 salary cap. Sure, without positional information we could have overlaps etc. but that’s an issue for a later version. Remember, version 1 should be the simplest implementation of your product.

马上，我们可以说出，对于一个简单的算法，鉴于我们的要求和约束，我们将发现以下几栏有用：ID，Salary和AvgPointsPerGame(幻想点)。 这将使我们能够选择“最佳”球员，同时保持在50,000美元的薪金上限以下。 当然，如果没有位置信息，我们可能会有重叠等，但这对于更高版本是一个问题。 请记住，版本1应该是产品的最简单实现。

Given this data, our first pass optimization algorithm can be broken up into the following simple steps:

有了这些数据，我们的首过优化算法可以分解为以下简单步骤：

1. Randomly select 8 players from the dataset.从数据集中随机选择8个玩家。
2. If the sum of the salaries of the players is greater than $50,000: go back to step 1 (too expensive).如果玩家的薪金总和超过50,000美元：请返回步骤1(太贵)。
3. Otherwise, sum the AvgPointsPerGame of each of the players in the roster and compare with a master maximum value. If greater, replace maximum value and roster.否则，对名册中每个玩家的AvgPointsPerGame求和，然后与主最大值进行比较。 如果更大，则替换最大值和花名册。
4. Unless all possible combinations have been explored, return to step 1. Once no more combinations, return the maximum value and the roster.除非已探究所有可能的组合，否则请返回步骤1。不再组合时，请返回最大值和花名册。

There we have it: a simple naive algorithm that picks 8 players in random that will have the maximum expected fantasy points while staying under the $50,000 salary cap. But this algorithm has a few glaring issues:

我们有一个简单的天真的算法，该算法随机选择8个玩家，这些玩家将具有最大的预期幻想积分，同时保持在50,000美元的薪金上限以下。 但是此算法存在一些明显的问题：

• No control regarding the position of the players. Hence the algorithm could generate a roster which consists of >3 of one position (G/F), in which case the roster would be invalid.无法控制玩家的位置。 因此，该算法可以生成由一个位置(G / F)> 3组成的花名册，在这种情况下，该花名册将无效。
• No check on players who are injured or not scheduled to play. This would result in a most definitive loss as all player points are important for a winning draft.不检查受伤或未安排比赛的球员。 这将导致最确定的损失，因为所有球员得分对获胜选秀都很重要。
• Lastly, the algorithm is very inefficient. Considering that we need to check each possible roster: for a given number of players n and roster size r, the number of possible rosters would be-最后，该算法效率很低。 考虑到我们需要检查每个可能的名册：对于给定数量的n个玩家和名册大小r，可能的名册数量为-

C( n , r ) = n! / (n — r)! . r!

C(n，r)= n！ /(n-r)！ 。 ！

To get an appreciation of this complexity, take a look at the table below which shows the number of checks if the total number of available players is 100.

要了解这种复杂性，请查看下表，该表显示了可用球员总数为100时的检查次数。

It’s safe to assume that our algorithm will take a VERY long time to output a roster of 8 players. But, because this is a first pass algorithm, we‘re happy with what we got. You can see the algorithm in action below, picking the top 5 players for a combined salary of $35,000. Not bad.

可以肯定地说，我们的算法将花费很长时间才能输出8名球员的花名册。 但是，由于这是首过算法，因此我们对所获得的结果感到满意。 您可以在下面看到该算法的运行情况，以最高薪水35,000美元选出前5名球员。 不错。

Because we’re on a mission to build a winning algorithm, let’s talk about version 2 optimizations.

因为我们肩负着构建成功算法的使命，所以让我们谈谈版本2优化。

算法版本2-中级体育博彩者 (Algorithm Version 2- Intermediate Sports Bettor)

Now, this is where our algorithm goes from being a naive optimizer to an intermediate-level sports bettor. Based on the drawbacks of version 1, and the factorial time complexity, I decided to implement a few data and algorithm level optimizations.

现在，这是我们的算法从单纯的优化器发展为中级体育博彩者的地方。 基于版本1的缺点和阶乘时间复杂度，我决定实施一些数据和算法级别的优化 。

First, I cleaned the data to only include players who’re confirmed to play games. This was an easy way to decrease the total number of available players from ~100 to ~85. This might look like a small increase, but in reality, for a roster of 8 players, our number of checks drastically decreases when the total number of players decreases. The change in the number of checks can be seen below.

首先，我清除了数据，只包括经确认可以玩游戏的玩家。 这是将可用玩家总数从100个减少至85个的简便方法。 这看似有点增加，但实际上，对于名额8人的名单，当总人数减少时，我们的支票数会急剧减少。 支票数量的变化可以在下面看到。

• C (100, 8) = 186,087,894,300C(100，8)= 186,087,894,300
• C (85, 8) = 48,124,511,370C(85，8)= 48,124,511,370

Our total number of operations (or checks) in the algorithm went down by ~75%!

我们在算法中的操作(或检查)总数下降了约75％！

Next up, I modified the algorithm itself to pick specific positions. Now, instead of picking every possible roster from the total number of players available, the algorithm picks 3 guards from only all available guards, followed by 3 forwards and lastly 1 center. As you can see, the total here is only 7 players and leaves the last pick to the user. This is a quick way to save some additional time on the algorithm as the user can manually find the best remaining player (highest expected points given the salary remaining).

接下来，我修改了算法本身以选择特定位置。 现在，该算法不再从可用球员总数中选择所有可能的花名册，而是仅从所有可用后卫中挑选3个后卫，然后是3个前锋和最后1个中锋。 如您所见，此处的总数仅为7位玩家，而最后的选择权留给了用户。 这是一种节省算法上额外时间的快速方法，因为用户可以手动找到剩余的最好的球员(给定剩余的薪水，可以获得最高的期望积分)。

This was a huge optimization because the number of guards vs the total number of players is ~40 vs 85. The number is similar for forwards and even less for centers. Note, there’s a slight overlap between the players in each category as some players play multiple positions but this was easy to deal with: I removed played who were already picked as Guards, before picking Forwards etc. The performance boost as a result of the above changes can be seen below:

这是一个巨大的优化，因为后卫人数与球员总数之比约为40比85。前锋的人数相似，中锋的人数更少。 请注意，每个类别中的玩家之间都有一点重叠，因为有些玩家扮演多个职位，但是这很容易解决：我删除了已经被选为后卫的角色，然后再选择Forwards等。由于上述原因，性能提升更改如下所示：

• C (85 , 8) = 48,124,511,370C(85，8)= 48,124,511,370
• C (40 , 3) x C (40 , 3) x C (20, 1) = 1,952,288,000C(40，3)x C(40，3)x C(20，1)= 1,952,288,000

This is huge. Now, the algorithm is conducting almost ~95% fewer operations and we have the best possible roster broken up by positions and under our salary cap. Let’s test our results!

这是巨大的。 现在，该算法的运算量减少了约95％，并且按职位和工资帽划分的人员名单可能最好。 让我们测试一下结果！

实际结果 (Real World Results)

If you’ve made it so far, congratulations. You’ve worked through the technical stuff, now it’s time for the results! I tried the algorithm’s pick over the course of three days on DK’s classic multiplier contests. Each time my entry fee was $1 and the payoff was $3 for the top 30% of the finishers. You can see the lineups generated by the algorithm and the results below.

到目前为止，如果您做到了，那就祝贺您。 您已经完成了技术性工作，现在是时候取得成果了！ 我在DK的经典乘数比赛中尝试了3天的算法选择。 每次我的报名费是1美元，而前30％的完成者的回报是3美元。 您可以在下面查看算法生成的阵容和结果。

As you can see from the above results, the real world outcomes of the competition have been good! Out of the three days that I created lineups using the algorithm, we lost twice and won once. Our intermediate-level sports bettor algorithm has done better than I expected, but there’s still a long way to go.

从以上结果可以看出，比赛的真实结果是不错的！ 在我使用算法创建阵容的三天内，我们输了两次，赢了一次。 我们的中级体育博彩算法比我预期的要好，但是还有很长的路要走。

I noticed few nuances about the results, including that our algorithm (before the v2 optimization) made a mistake on day 1 where an injured player was drafted into the team (P. Beverley) which resulted in a weak draft. This was fixed in version 2 and will not be repeated again. Additionally, once cool thing has been that despite the mixed results, the algorithm has consistently created lineups which get >200 fantasy points, which is pretty high!

我注意到关于结果的细微差别，包括我们的算法(在v2优化之前)在第1天犯了一个错误，即一名受伤的球员被征召入队(P. Beverley)，导致选秀不力。 此问题在版本2中已修复，将不再重复。 此外，一旦出现有趣的结果是，尽管得到了混合结果，该算法仍会持续创建阵容，获得超过200个幻想点，这是非常高的！

下一步是什么？ (What’s next?)

Well, there you have it. So far, I’ve spent $3 on entree fees and made $3 on winnings, for a grand total of $0 change! I have $25 left to spend on this project before my inner alarm bells start ringing, so I clearly need to improve this algorithm. After talking to some of my friends, who know a lot more about basketball than myself, I have a few hypotheses to test out. Some of these include:

好吧，那里有。 到目前为止，我已经在主菜费用上花费了$ 3，并在奖金中赚了$ 3，总共有$ 0的找零！ 在我的内部警钟开始鸣响之前，我还有25美元可用于该项目，所以我显然需要改进此算法。 与我的一些朋友交谈后，我比我更了解篮球，我有一些假设可以检验。 其中一些包括：

• Using additional player data over the last n games. This way the model would have more context, instead of just a snapshot value

  在过去n场比赛中使用其他玩家数据。 这样，模型将具有更多上下文，而不仅仅是快照值

• Using prior team match-up data to adjust weights placed on certain games. For example, this could help avoid picking a player in a match-up where (based on previous meets) the player has failed to perform使用先前的球队比赛数据来调整某些游戏的权重。 例如，这可以帮助避免在对战中选择一名球员(基于先前的见面)而该球员未能完成比赛
• Exploring dual optimization strategies探索双重优化策略

And more! If you have any ideas about how to improve this project please feel free to reach out to me on LinkedIn or over email which you can find on my Website. Additionally, all the data and code for this project can be found on my Github repository, so feel free to clone/fork it and test your own hypotheses! And, as always, any and all feedback is greatly appreciated.

和更多！ 如果您对如何改善此项目有任何想法，请随时通过LinkedIn或通过我的网站上找到的电子邮件与我联系。 此外，该项目的所有数据和代码都可以在我的Github存储库中找到，因此随时可以克隆/分叉它并测试自己的假设！ 而且，一如既往，我们非常感谢任何反馈。

Stay safe out there everyone and keep building cool stuff.

每个人都应该保持安全，并继续制作有趣的东西。